Sampling From Dense Streams Without Penalty: Improved Bounds For Frequency Moments And Heavy Hitters

We investigate the ability to sample relatively small amounts of data from a stream and approximately calculate statistics on the original stream. Mc-Gregor et al. [29] provide worst case theoretical bounds that show space costs for sampling that are inversely correlated with the sampling rate. Indeed, while the lower bound of McGregor et al. cannot be improved in the general case, we show it is possible to improve the space bound for stream D of domain n, when the average positive frequency mu = F-1/F-0 is sufficiently large. We consider the following range of parameters: mu >= log (n) and sample rate p >= C-k mu(-1) log (n), where C-k is a constant. On these streams we improve the bound from (O) over tilde (1/pn(1-2/k)) to (O) over tilde (1/pn(1-2/k)) 0) thus giving polynomial improvement in space for sufficiently large /1 and p(-1).